This document provides a summary of the change-point analysis for Dengue (dengue).
The following section summarizes change-point analysis for trends in the number of visits before diagnosis using the standard piecewise-modeling approach to find the change-point. Specifically, we evaluate 4 peicewise models with linear, quadratic, cubic and exponential trends. The change-point is found by iterating over different change-points and selecting the best fitting model based on AIC.
This section summarizes results using counts of SSD visits.
| label | Change Point | Pred. Bound CP | CP # Miss | PB CP # Miss |
|---|---|---|---|---|
| Piecewise lm w/ periodicity | 7 | 18 | 1966.45 | 2452.60 |
| Piecewise lm | 7 | 18 | 1964.66 | 2444.54 |
| Piecewise quad w/ periodicity | 14 | 18 | 2214.20 | 2300.31 |
| Piecewise quad | 14 | 16 | 2208.73 | 2285.39 |
| Piecewise cubic w/ periodicity | 14 | 16 | 1935.21 | 1985.90 |
| Piecewise cubic | 21 | 16 | 2199.16 | 2173.21 |
| Piecewise exp w/ periodicity | 14 | 18 | 2045.31 | 2135.55 |
| Piecewise exp | 14 | 16 | 2038.02 | 2115.18 |
| label | Change Point | Pred. Bound CP | CP Consisency | MSE | MSE 7-day | MSE 14-day |
|---|---|---|---|---|---|---|
| Piecewise lm w/ periodicity | 7 | 18 | -157.14286 | 276.79 | 4820.68 | 2813.04 |
| Piecewise lm | 7 | 18 | -157.14286 | 286.42 | 5038.98 | 2998.57 |
| Piecewise quad w/ periodicity | 14 | 18 | -28.57143 | 67.94 | 603.23 | 310.85 |
| Piecewise quad | 14 | 16 | -14.28571 | 77.60 | 746.17 | 400.24 |
| Piecewise cubic w/ periodicity | 14 | 16 | -14.28571 | 45.83 | 315.66 | 170.16 |
| Piecewise cubic | 21 | 16 | 23.80952 | 42.35 | 49.13 | 79.89 |
| Piecewise exp w/ periodicity | 14 | 18 | -28.57143 | 71.27 | 647.28 | 342.43 |
| Piecewise exp | 14 | 16 | -14.28571 | 81.86 | 745.93 | 404.87 |
| label | Change Point | Pred. Bound CP | Average Rank | consistency_rank | mse_rank | mse7_rank | mse14_rank |
|---|---|---|---|---|---|---|---|
| Piecewise cubic | 21 | 16 | 1.25 | 2 | 1 | 1 | 1 |
| Piecewise cubic w/ periodicity | 14 | 16 | 1.75 | 1 | 2 | 2 | 2 |
| Piecewise quad w/ periodicity | 14 | 18 | 3.00 | 3 | 3 | 3 | 3 |
| Piecewise exp w/ periodicity | 14 | 18 | 3.75 | 3 | 4 | 4 | 4 |
| Piecewise quad | 14 | 16 | 4.25 | 1 | 5 | 6 | 5 |
| Piecewise exp | 14 | 16 | 4.50 | 1 | 6 | 5 | 6 |
| Piecewise lm w/ periodicity | 7 | 18 | 6.25 | 4 | 7 | 7 | 7 |
| Piecewise lm | 7 | 18 | 7.00 | 4 | 8 | 8 | 8 |
This section summarizes results using counts of all visits.
| label | Change Point | Pred. Bound CP | CP # Miss | PB CP # Miss |
|---|---|---|---|---|
| Piecewise lm w/ periodicity | 7 | 16 | 2262.02 | 2692.39 |
| Piecewise lm | 7 | 16 | 2253.96 | 2667.72 |
| Piecewise quad w/ periodicity | 14 | 16 | 2548.36 | 2585.93 |
| Piecewise quad | 14 | 16 | 2529.15 | 2558.58 |
| Piecewise cubic w/ periodicity | 14 | 16 | 2217.03 | 2230.57 |
| Piecewise cubic | 14 | 9 | 2157.79 | 2038.04 |
| Piecewise exp w/ periodicity | 14 | 16 | 2311.97 | 2348.18 |
| Piecewise exp | 14 | 16 | 2269.79 | 2293.44 |
| label | Change Point | Pred. Bound CP | CP Consisency | MSE | MSE 7-day | MSE 14-day |
|---|---|---|---|---|---|---|
| Piecewise lm w/ periodicity | 7 | 16 | -128.57143 | 428.06 | 5709.82 | 3230.02 |
| Piecewise lm | 7 | 16 | -128.57143 | 1013.28 | 7904.00 | 5058.27 |
| Piecewise quad w/ periodicity | 14 | 16 | -14.28571 | 223.22 | 657.65 | 450.33 |
| Piecewise quad | 14 | 16 | -14.28571 | 805.89 | 2065.18 | 1706.23 |
| Piecewise cubic w/ periodicity | 14 | 16 | -14.28571 | 193.28 | 335.52 | 298.62 |
| Piecewise cubic | 14 | 9 | 35.71429 | 778.97 | 1668.22 | 1493.67 |
| Piecewise exp w/ periodicity | 14 | 16 | -14.28571 | 214.76 | 607.93 | 432.73 |
| Piecewise exp | 14 | 16 | -14.28571 | 797.80 | 1931.53 | 1626.87 |
| label | Change Point | Pred. Bound CP | Average Rank | consistency_rank | mse_rank | mse7_rank | mse14_rank |
|---|---|---|---|---|---|---|---|
| Piecewise cubic w/ periodicity | 14 | 16 | 1.00 | 1 | 1 | 1 | 1 |
| Piecewise exp w/ periodicity | 14 | 16 | 1.75 | 1 | 2 | 2 | 2 |
| Piecewise quad w/ periodicity | 14 | 16 | 2.50 | 1 | 3 | 3 | 3 |
| Piecewise cubic | 14 | 9 | 3.75 | 2 | 5 | 4 | 4 |
| Piecewise exp | 14 | 16 | 4.25 | 1 | 6 | 5 | 5 |
| Piecewise quad | 14 | 16 | 5.00 | 1 | 7 | 6 | 6 |
| Piecewise lm w/ periodicity | 7 | 16 | 5.25 | 3 | 4 | 7 | 7 |
| Piecewise lm | 7 | 16 | 6.75 | 3 | 8 | 8 | 8 |
This section summarizes results using counts of SSD-related visits.
The following figure depicts the in-sample and out-of-sample performance (MSE) of various bounds on the opportunity window and different trends.
The following table depicts the top 10 specifications based on either aggregate or k-fold out-of-sample performance:
| rank | Bound (Days) | Model | MSE | Bound (Days) | Model | MSE |
|---|---|---|---|---|---|---|
| 1 | 14 | Cubic | 64.17 | 14 | Cubic | 116.61 |
| 2 | 21 | Cubic | 65.19 | 21 | Cubic | 118.62 |
| 3 | 21 | Quadratic | 71.29 | 21 | Quadratic | 125.26 |
| 4 | 14 | Quadratic | 82.35 | 14 | Quadratic | 134.84 |
| 5 | 7 | Cubic | 87.36 | 7 | Cubic | 138.91 |
| 6 | 21 | Linear | 90.08 | 21 | Linear | 145.03 |
| 7 | 28 | Cubic | 103.50 | 28 | Cubic | 157.84 |
| 8 | 28 | Quadratic | 105.53 | 28 | Quadratic | 160.12 |
| 9 | 28 | Linear | 113.33 | 28 | Linear | 168.30 |
| 10 | 14 | Linear | 128.36 | 14 | Linear | 181.44 |
The following figure depicts the observed and expected trend for the top 4 models based on aggregate out-of-sample performance:
The following figure depicts the observed and expected trend for the top 4 models based on 99-fold out-of-sample performance:
The following table depicts the 10 best models for each trend, based on aggregate out-of-sample performance:
| Rank | Bound | MSE | Bound | MSE | Bound | MSE |
|---|---|---|---|---|---|---|
| 1 | 21 | 90.08 | 21 | 71.29 | 14 | 64.17 |
| 2 | 28 | 113.33 | 14 | 82.35 | 21 | 65.19 |
| 3 | 14 | 128.36 | 28 | 105.53 | 7 | 87.36 |
| 4 | 35 | 178.93 | 7 | 148.22 | 28 | 103.50 |
| 5 | 42 | 255.55 | 35 | 175.42 | 35 | 174.80 |
| 6 | 7 | 278.60 | 42 | 254.01 | 42 | 253.85 |
| 7 | 49 | 346.96 | 49 | 346.20 | 49 | 346.06 |
| 8 | 56 | 452.28 | 56 | 451.94 | 56 | 451.28 |
| 9 | 63 | 539.72 | 63 | 539.61 | 63 | 537.85 |
| 10 | 70 | 626.87 | 70 | 627.38 | 70 | 626.73 |
The following table depicts the 10 best models for each trend, based on 99-fold out-of-sample performance:
| Rank | Bound | MSE | Bound | MSE | Bound | MSE |
|---|---|---|---|---|---|---|
| 1 | 21 | 145.03 | 21 | 125.26 | 14 | 116.61 |
| 2 | 28 | 168.30 | 14 | 134.84 | 21 | 118.62 |
| 3 | 14 | 181.44 | 28 | 160.12 | 7 | 138.91 |
| 4 | 35 | 234.75 | 7 | 199.65 | 28 | 157.84 |
| 5 | 42 | 311.75 | 35 | 230.96 | 35 | 230.08 |
| 6 | 7 | 330.85 | 42 | 310.18 | 42 | 309.92 |
| 7 | 49 | 403.77 | 49 | 403.05 | 49 | 402.86 |
| 8 | 56 | 509.84 | 56 | 509.62 | 56 | 509.01 |
| 9 | 63 | 598.07 | 63 | 598.10 | 63 | 596.51 |
| 10 | 70 | 686.45 | 70 | 686.98 | 70 | 686.39 |
The following figure depicts the top 4 performing linear models based on aggregate out-of-sample MSE:
The following figure depicts the top 4 performing linear models based on 99-fold out-of-sample MSE:
The following figure depicts the top 4 performing quadratic models based on aggregate out-of-sample MSE:
The following figure depicts the top 4 performing quadratic models based on 99-fold out-of-sample MSE:
The following figure depicts the top 4 performing cubic models based on aggregate out-of-sample MSE:
The following figure depicts the top 4 performing cubic models based on 99-fold out-of-sample MSE:
This section summarizes results using counts of all visits.
The following figure depicts the in-sample and out-of-sample performance of various bounds on the opportunity window and different trends.
The following table depicts the top 10 specifications based on both aggregate and k-fold out-of-sample performance:
| rank | Bound (Days) | Model | MSE | Bound (Days) | Model | MSE |
|---|---|---|---|---|---|---|
| 1 | 14 | Cubic | 245.82 | 14 | Cubic | 460.33 |
| 2 | 21 | Cubic | 263.96 | 21 | Cubic | 479.69 |
| 3 | 14 | Quadratic | 268.61 | 14 | Quadratic | 481.77 |
| 4 | 7 | Cubic | 270.26 | 7 | Cubic | 484.25 |
| 5 | 21 | Quadratic | 274.50 | 21 | Quadratic | 489.58 |
| 6 | 21 | Linear | 285.11 | 21 | Linear | 498.92 |
| 7 | 14 | Linear | 301.38 | 14 | Linear | 511.66 |
| 8 | 28 | Cubic | 326.82 | 28 | Cubic | 544.89 |
| 9 | 28 | Quadratic | 333.87 | 28 | Quadratic | 551.43 |
| 10 | 28 | Linear | 336.69 | 28 | Linear | 553.55 |
The following figure depicts the observed and expected trend for the top 4 models based on aggregate out-of-sample performance:
The following figure depicts the observed and expected trend for the top 4 models based on k-fold out-of-sample performance:
The following table depicts the 10 best models for each trend, based on aggregate out-of-sample performance:
| Rank | Bound | MSE | Bound | MSE | Bound | MSE |
|---|---|---|---|---|---|---|
| 1 | 21 | 285.11 | 14 | 268.61 | 14 | 245.82 |
| 2 | 14 | 301.38 | 21 | 274.50 | 21 | 263.96 |
| 3 | 28 | 336.69 | 28 | 333.87 | 7 | 270.26 |
| 4 | 35 | 419.88 | 7 | 344.01 | 28 | 326.82 |
| 5 | 7 | 457.67 | 35 | 421.30 | 35 | 418.23 |
| 6 | 42 | 525.85 | 42 | 528.22 | 42 | 529.45 |
| 7 | 49 | 658.32 | 49 | 660.70 | 49 | 660.03 |
| 8 | 56 | 812.12 | 56 | 814.68 | 56 | 813.87 |
| 9 | 63 | 948.60 | 63 | 950.59 | 63 | 950.15 |
| 10 | 70 | 1087.20 | 70 | 1086.70 | 70 | 1088.31 |
The following table depicts the 10 best models for each trend, based on 99-fold out-of-sample performance:
| Rank | Bound | MSE | Bound | MSE | Bound | MSE |
|---|---|---|---|---|---|---|
| 1 | 21 | 498.92 | 14 | 481.77 | 14 | 460.33 |
| 2 | 14 | 511.66 | 21 | 489.58 | 21 | 479.69 |
| 3 | 28 | 553.55 | 28 | 551.43 | 7 | 484.25 |
| 4 | 35 | 638.22 | 7 | 556.84 | 28 | 544.89 |
| 5 | 7 | 665.62 | 35 | 639.91 | 35 | 637.14 |
| 6 | 42 | 744.27 | 42 | 746.61 | 42 | 747.99 |
| 7 | 49 | 875.85 | 49 | 878.29 | 49 | 877.91 |
| 8 | 56 | 1027.95 | 56 | 1030.54 | 56 | 1030.03 |
| 9 | 63 | 1163.36 | 63 | 1165.32 | 63 | 1165.27 |
| 10 | 70 | 1301.27 | 70 | 1300.55 | 70 | 1302.09 |
The following figure depicts the top 4 performing linear models based on out-of-sample MSE
The following figure depicts the top 4 performing quadratic models based on out-of-sample MSE
The following figure depicts the top 4 performing cubic models based on out-of-sample MSE